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CAT 2019 Slot 1 — QA Question 23

PercentageEasy

In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys, pass an examination, the percentage of the girls who do not pass is

Answer & solution

Answer: 20

Solution

Easy

Let total be 100x100x; girls 60x60x, boys 40x40x. The "30 more girls than boys" condition fixes xx (and the actual head-counts). Then count passers: 68%68\% pass, 3030 of them boys, so the rest are girls — subtract to get girls who failed, as a percentage of all girls.

1

Fix the numbers. Girls =60x=60x, boys =40x=40x, with 30 more girls.

60x=40x+30⇒ 20x=30 ⇒ x=32\begin{aligned} &60x=40x+30\\ &\Rightarrow\ 20x=30\ \Rightarrow\ x=\tfrac{3}{2} \end{aligned}
2

Head-counts. Substitute x=32x=\tfrac{3}{2}.

girls=60x=90,boys=40x=60,total=150\begin{aligned} &\text{girls}=60x=90,\quad \text{boys}=40x=60,\quad \text{total}=150 \end{aligned}
3

Count the passers. 68%68\% pass; 3030 of them are boys.

passed=68%×150=102⇒ girls passed=102−30=72\begin{aligned} &\text{passed}=68\%\times150=102\\ &\Rightarrow\ \text{girls passed}=102-30=72 \end{aligned}
4

Girls who did not pass, as a percentage. Out of 9090 girls.

girls failed=90−72=18⇒ 1890×100=20%\begin{aligned} &\text{girls failed}=90-72=18\\ &\Rightarrow\ \frac{18}{90}\times100=20\% \end{aligned}
Girls who do not pass=20%\text{Girls who do not pass}=20\%
CAT 2019 Slot 1 QA Q23: In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of — Solution | TheCATExam